A107381 a(n) = 4*a(n-1)-3*a(n-2) -3*a(n-3) +2*a(n-4) + a(n-5), n>7.

4, 3, 9, 17, 40, 92, 215, 506, 1200, 2861, 6848, 16436, 39523, 95162, 229328, 552977, 1333920, 3218612, 7767575, 18747986, 45254200, 109241261, 263712248, 636626156, 1536900483, 3710323442

Offset

0,1

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (4,-3,-3,2,1).

Formula

G.f.: (-2*x^3+3*x^6+x^7-9*x^2+13*x-4)/((x-1)* (x^2+x-1) * (x^2+2*x-1) ). [Sep 28 2009]

a(n) = 1+A000032(n) + A002203(n), n>2 [Sep 28 2009].

Mathematica

n = 3; b4 = x /. NSolve[x^4 - n*x^3 + n*x + 1 == 0, x][[4]] b3 = x /. NSolve[x^4 - n*x^3 + n*x + 1 == 0, x][[3]] b2 = x /. NSolve[x^4 - n*x^3 + n*x + 1 == 0, x][[2]] b1 = x /. NSolve[x^4 - n*x^3 + n*x + 1 == 0, x][[1]] digits = 25 a = Table[n*(b4^m + b3^m + b1^m + b2^m)/ (b4 + b3 + b2 + b1), {n, 0, digits}]

Crossrefs

Sequence in context: A187770 A103218 A319311 * A242531 A275160 A363469

Adjacent sequences: A107378 A107379 A107380 * A107382 A107383 A107384

Keyword

nonn,easy

Author

Roger L. Bagula, May 24 2005

Extensions

Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009

Status

approved